Problem: Simplify the following expression: $\dfrac{63q}{70q^4}$ You can assume $q \neq 0$.
$ \dfrac{63q}{70q^4} = \dfrac{63}{70} \cdot \dfrac{q}{q^4} $ To simplify $\frac{63}{70}$ , find the greatest common factor (GCD) of $63$ and $70$ $63 = 3 \cdot 3 \cdot 7$ $70 = 2 \cdot 5 \cdot 7$ $ \mbox{GCD}(63, 70) = 7 $ $ \dfrac{63}{70} \cdot \dfrac{q}{q^4} = \dfrac{7 \cdot 9}{7 \cdot 10} \cdot \dfrac{q}{q^4} $ $\phantom{ \dfrac{63}{70} \cdot \dfrac{1}{4}} = \dfrac{9}{10} \cdot \dfrac{q}{q^4} $ $ \dfrac{q}{q^4} = \dfrac{q}{q \cdot q \cdot q \cdot q} = \dfrac{1}{q^3} $ $ \dfrac{9}{10} \cdot \dfrac{1}{q^3} = \dfrac{9}{10q^3} $